On the existence and uniqueness of the solution of the one-dimensional bounce problem

1982 ◽  
Vol 52 (1) ◽  
pp. 619-626
Author(s):  
Giovanni Prouse ◽  
Francesca Rolandi
Keyword(s):  
Existence And Uniqueness ◽  
One Dimensional ◽  
Uniqueness Of The Solution ◽  
The One

THE SCALAR KELLER–SEGEL MODEL ON NETWORKS

2013 ◽  
Vol 24 (02) ◽  
pp. 221-247 ◽  
Author(s):  
R. BORSCHE ◽  
S. GÖTTLICH ◽  
A. KLAR ◽  
P. SCHILLEN
Keyword(s):  
Network Model ◽  
Existence And Uniqueness ◽  
Computational Studies ◽  
One Dimensional ◽  
First Order ◽  
General Network ◽  
Uniqueness Of The Solution ◽  
Order Scheme ◽  
Network Topologies ◽  
The One

In this work, we extend the one-dimensional Keller–Segel model for chemotaxis to general network topologies. We define appropriate coupling conditions ensuring the conservation of mass and show the existence and uniqueness of the solution. For our computational studies, we use a positive preserving first-order scheme satisfying a network CFL condition. Finally, we numerically validate the Keller–Segel network model and present results regarding special network geometries.

scholarly journals Analytical results in transient brush tyre models: theory for large camber angles and classic solutions with limited friction

Meccanica ◽  
2021 ◽  
Author(s):  
Luigi Romano ◽  
Francesco Timpone ◽  
Fredrik Bruzelius ◽  
Bengt Jacobson
Keyword(s):  
Rolling Direction ◽  
State Theory ◽  
General Situation ◽  
Linear Dynamical Systems ◽  
Transient Conditions ◽  
One Dimensional ◽  
Analytical Results ◽  
Classic Theory ◽  
Uniqueness Of The Solution ◽  
The One

AbstractThis paper establishes new analytical results in the mathematical theory of brush tyre models. In the first part, the exact problem which considers large camber angles is analysed from the perspective of linear dynamical systems. Under the assumption of vanishing sliding, the most salient properties of the model are discussed with some insights on concepts as existence and uniqueness of the solution. A comparison against the classic steady-state theory suggests that the latter represents a very good approximation even in case of large camber angles. Furthermore, in respect to the classic theory, the more general situation of limited friction is explored. It is demonstrated that, in transient conditions, exact sliding solutions can be determined for all the one-dimensional problems. For the case of pure lateral slip, the investigation is conducted under the assumption of a strictly concave pressure distribution in the rolling direction.

Smooth solution to the one-dimensional inhomogeneous non-automorphic Landau–Lifshitz equation

2006 ◽  
Vol 462 (2072) ◽  
pp. 2397-2413 ◽  
Author(s):  
Junyu Lin ◽  
Shijin Ding
Keyword(s):  
Difference Method ◽  
Existence And Uniqueness ◽  
Smooth Solution ◽  
One Dimension ◽  
Initial Value ◽  
One Dimensional ◽  
Uniform Estimates ◽  
Lifshitz Equation ◽  
Orthogonal Base ◽  
The One

Using the differential–difference method and viscosity vanishing approach, we obtain the existence and uniqueness of the global smooth solution to the periodic initial-value problem of the inhomogeneous, non-automorphic Landau–Lifshitz equation without Gilbert damping terms in one dimension. To establish the uniform estimates, we use some identities resulting from the fact and the fact that the vectors form an orthogonal base of the space .

scholarly journals On the thermoelasticity with two porosities: asymptotic behaviour

2018 ◽  
Vol 24 (9) ◽  
pp. 2713-2725 ◽  
Author(s):  
N. Bazarra ◽  
J.R. Fernández ◽  
M.C. Leseduarte ◽  
A. Magaña ◽  
R. Quintanilla
Keyword(s):  
Asymptotic Stability ◽  
Exponential Decay ◽  
Existence And Uniqueness ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Uniqueness Result ◽  
Porous Structures ◽  
One Dimensional ◽  
Dimensional Version ◽  
The One

In this paper we consider the one-dimensional version of thermoelasticity with two porous structures and porous dissipation on one or both of them. We first give an existence and uniqueness result by means of semigroup theory. Exponential decay of the solutions is obtained when porous dissipation is assumed for each porous structure. Later, we consider dissipation only on one of the porous structures and we prove that, under appropriate conditions on the coefficients, there exists undamped solutions. Therefore, asymptotic stability cannot be expected in general. However, we are able to give suitable sufficient conditions for the constitutive coefficients to guarantee the exponential decay of the solutions.

scholarly journals A LARGE DEFORMATION, VISCOELASTIC, THIN ROD MODEL: DERIVATION AND ANALYSIS

2009 ◽  
Vol 19 (10) ◽  
pp. 1907-1928 ◽  
Author(s):  
J. BEYROUTHY ◽  
H. LE DRET
Keyword(s):  
Existence And Uniqueness ◽  
Finite Strain ◽  
Three Dimensional ◽  
Evolution Problem ◽  
Well Posedness ◽  
One Dimensional ◽  
Uniqueness Of The Solution ◽  
Model Derivation ◽  
Regularity Results ◽  
Strain Model

We present a Cosserat-based three-dimensional to one-dimensional reduction in the case of a thin rod, of the viscoelastic finite strain model introduced by Neff. This model is a coupled minimization/evolution problem. We prove the existence and uniqueness of the solution of the reduced minimization problem. We also show a few regularity results for this solution which allow us to establish the well-posedness of the evolution problem. Finally, the reduced model preserves observer invariance.

scholarly journals Existence, uniqueness and numerical solution of a fractional PDE with integral conditions

2019 ◽  
Vol 24 (3) ◽  
pp. 368-386
Author(s):  
Jesus Martín-Vaquero ◽  
Ahcene Merad
Keyword(s):  
Existence And Uniqueness ◽  
Recent Literature ◽  
Numerical Approach ◽  
Integral Conditions ◽  
Fractional Partial Differential Equation ◽  
One Dimensional ◽  
Fractional Pde ◽  
Uniqueness Of The Solution ◽  
Nonlocal Integral Conditions ◽  
Hereditary Properties

This paper is devoted to the solution of one-dimensional Fractional Partial Differential Equation (FPDE) with nonlocal integral conditions. These FPDEs have been of considerable interest in the recent literature because fractional-order derivatives and integrals enable the description of the memory and hereditary properties of different substances. Existence and uniqueness of the solution of this FPDE are demonstrated. As for the numerical approach, a Galerkin method based on least squares is considered. The numerical examples illustrate the fast convergence of this technique and show the efficiency of the proposed method.

scholarly journals INVESTIGATION OF STATIONARY SOLUTIONS OF VISCOELASTIC MELT SPINNING EQUATIONS AND STABILITY WITH RESPECT TO INCREASING VISCOELASTICITY

2010 ◽  
Vol 15 (3) ◽  
pp. 287-298 ◽  
Author(s):  
R. Dhadwal ◽  
S. K. Kudtarkar
Keyword(s):  
Constitutive Equation ◽  
Numerical Simulations ◽  
Existence And Uniqueness ◽  
Melt Spinning ◽  
Stationary Solutions ◽  
Model Parameter ◽  
One Dimensional ◽  
Spinning Process ◽  
The Stability ◽  
The One

The one‐dimensional equations governing the formation of viscoelastic fibers using Giesekus constitutive equation were studied. Existence and uniqueness of stationary solutions was shown and relation between the stress at the spinneret and the take‐up velocity was found. Further, the value of the Giesekus model parameter for which the fibre exhibits Newtonian behaviour was found analytically. Using numerical simulations it was shown that below this value of the parameter the fluid shows extension thickening behaviour and above, extension thinning. In this context, by simulating the non‐stationary equations the effect of viscoelasticity on the stability of the spinning process was studied.

Asymptotic behaviour of solutions of the hydrodynamic model of semiconductors

2002 ◽  
Vol 132 (2) ◽  
pp. 359-378 ◽  
Author(s):  
Hailiang Li ◽  
Peter Markowich ◽  
Ming Mei
Keyword(s):  
Steady State ◽  
Asymptotic Behaviour ◽  
Small Perturbation ◽  
Hydrodynamic Model ◽  
Existence And Uniqueness ◽  
Steady State Solution ◽  
State Solution ◽  
Energy Estimates ◽  
One Dimensional ◽  
The One

Degond and Markowich discussed the existence and uniqueness of a steady-state solution in the subsonic case for the one-dimensional hydrodynamic model of semiconductors. In the present paper, we reconsider the existence and uniqueness of a globally smooth subsonic steady-state solution, and prove its stability for small perturbation. The proof method we adopt in this paper is based on elementary energy estimates.

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